I'm not a lawyer, but I think we're entering into a legal gray area. There are the existing frameworks of copyright, parody, free speech, slander, libel, etc. that are all somewhat tangential to this.
I believe (I'm not certain) that celebrity voice impersonation is legal as long as it is not used to sell or endorse a product.
Most models are trained on the original speaker's voice, but maybe only a little bit. Models might incorporate learning from many speakers. We might even be able to boil down a speaker representation to a small vector encoding in the future. It'll be interesting if we can capture the representation of a person with just a few numbers.
I don't think the legislature should be overly protective against machine learning. It seems obvious to me that neural networks will play a huge role in creating entirely virtual musicians and influencers. We're already seeing this start to happen. r9y9 on github has published some models that rival Vocaloid in lyrical ability.
At the same time, we don't want these techniques used to commit fraud, slander, or have them be used to falsely accuse someone of committing some act. These are things we might need new legal protections for.
But I don't know what I'm talking about. I'm not a lawyer.